Project Report 2013 MVK160 Heat and Mass Transport May 13, 2013, Lund, Sweden Effects of mass transfer processes in designing a heterogeneous catalytic reactor Maryneth de Roxas Dept. of Energy Sciences, Faculty of Engineering, Lund University, Box 118, 22100 Lund, Sweden ABSTRACT Heterogeneous catalytic reactors are widely used in the chemical industry mainly because of their economical advantages. The presence of solid catalyst makes the transport processes prominent. The aim of this study is to demonstrate the importance of transport processes in designing a heterogeneous catalytic reactor. The focus is narrowed down to the mass transfers processes. Two different regimes can be identified: external and internal mass transfers. To highlight their effects, the amount of catalyst needed for a 90% conversion of an irreversible gas- solid reaction is calculated. Different cases are considered: the mass transfers were neglected; only the external mass transfer was considered; only the internal mass transfer was considered and both mass transfer regimes were taken into account. The results show that when mass transfers are considered the amount of catalyst needed increases. In the studied case the dominating mass transfer regime is the internal mass transfer. The amount of catalyst was nine times larger compared to when no mass transfer was considered. This simple consideration shows how transport processes influences the process and the design considerably. NOMENCLATURE A Cross section area of the reactor A cat Catalyst particle surface area C Molar concentration d Diameter D m Diffusion coefficient D eff Effective diffusion coefficient G Volumetric fluid flow rate k Reaction rate coefficient k G External mass transfer coefficient M Mean molecular mass n Degree of reaction N Molar flux P Pressure P i Partial pressure T Temperature r i Reaction rate r radius 1 R Re Sc v V W cat X Gas constant Reynold s number Schmidt number Axial velocity in the reactor Volume Amount of catalyst Conversion Greek Symbols δ Fluid film thickness ε Catalyst porosity η Effectiveness factor μ Fluid viscosity ρ Density τ Residence time in the reactor ϕ Thiele modulus Subscripts 0 Feed or inlet cat Catalyst f Fluid i Reactant obs Observed Superscripts ext External int Internal b Bulk fluid s Catalyst surface INTRODUCTION In today s chemical industry, catalytic processes are highly dominant. They account for about 90% of the chemical and refining processes [1]. A catalytic process involves a catalyst, a chemical compound that facilitates a chemical reaction without being consumed in the process [2]. They are used not only in the chemical bulk industry, oil refining and petrochemical industry [2], but also in food production, pharmaceutical industry and a lot more [1]. The majority of the catalytic reactions are heterogeneous, in which the catalyst are in solid for and the
reacting compounds in a fluid form. This is mainly because heterogeneous catalysts are easier to recover and recycle making them more economical. A typical example is the use of iron- based catalysts in the manufacturing of ammonia. Another example is the use of noble metals to convert monoxide to carbon dioxide to clean automotive exhaust gases [2]. Catalysts used in the industry are mainly porous solid particles. For the reaction to occur, the reacting species need to be diffused on the active surface of the catalyst. For this reason, the effects of transport processes become more considerable [2]. Thus, the reaction calculations become more complicated. Due to the molecular diffusion required, the concentrations of the reactants in the active sites are much lower than the concentrations of the bulk fluid entering the reactor [2]. This concentration gradient in the catalyst affects the reaction rate [1]. Consequently, the transport processes should be taken into account in designing a heterogeneous reactor, both for calculating the amount of catalyst needed and in estimating the performance of the reactor [1]. This paper, aims to show the effects of the transport processes in designing a heterogeneous catalytic reactor. The main focus is on the mass transfer process, in which both external and internal mass transfers will be studied. To highlight the importance of these transport processes, the amount of catalyst required for a given study reaction was be calculated for different cases. The results were then compared and discussed. Fig. 1. Typical packed bed reactor. [2]. As mentioned earlier, typical catalysts are porous solids. They are in pellet form, composed of an interconnecting pore inside the catalyst. The active particles are mostly located on the walls of the pores [1]. The reactants then need to be transported from the bulk fluid to the interior of the catalysts for the reaction to take place. Figure 2 shows a schematic drawing of the catalyst in the reactor at different scales. PROBLEM STATEMENT The most commonly applied reactor for heterogeneous catalytic processes is a packed bed reactor. The typical packed bed reactor is a plug flow reactor in which catalyst particles are placed inside. The catalysts would remain stagnant while reactants in fluid form are passed through [2]. Figure 1 shows an example of a typical packed bed reactor. Fig. 2. Different size scales in a packed bed reactor [3]. There are two transport regimes that need to be considered. First, the reactants need to be transported from the bulk fluid to the outer surface of the catalyst. This is called the external or interparticle transport. Second, the reactants need to be diffused inside the pores. This is known as the internal or intraparticle transport. Both the transport mechanism and the transport rates are different for the two regimes. Thus, different variables influence the two regimes. Both transport regimes offers diffusion resistances to the mass transfer. This is the cause of the lower concentrations of reactants inside the catalyst pores 2
compared to the bulk concentration [2]. As mentioned before, the concentration gradients on the surface and inside the catalyst influence the reaction rate of the process [1]. Furthermore, these gradients serve as the driving force of the reactant against the resistances mass transfer [2]. Figure 3 shows the changes of the concentration profile due to the external and internal mass transfers. mass transfer is considered and finally (d) both internal and external mass transfers are considered. For this paper a catalyzed irreversible gas- solid reaction that was studied in a tubular reactor is considered [5]. The experimental data acquired are presented in Table 1. Table 1. Acquired data for the reaction [5]. A =2 dm ρ cat =0.8 g/cm 3 G 0 = 14.4 m 3 /h (20% reactant, 80% inert) T 0 = 390 K D ext m,i =0.1 cm 2 /s P 0 = 3.2 atm D int eff,i = 0.001 cm 2 /s M = 30 g/mol r cat = 5 mm μ =190 10-7 Pa s ε = 0.3 The reaction rate was also determined and the expression is presented in equation 1 [5]. r i = 0.4080 C i 2 mol/l s (1) Fig. 3. Changes in the concentration profiles from the bulk fluid to the interior of the catalyst particle [1]. LITERATURE SURVEY Michael Faraday made the discovery of the catalytic effect. He observed that oxidation reactions were enhanced by the presence of a metal powder. In 1836, Jacob Berzelius first described the catalytic effect [2]. Empirical observations then accumulated and several important catalytic processes were developed [4]. To this day, experimental observations are carried out to find the appropriate catalyst for different reactions. Furthermore, studies are also being carried out to improve the catalysts themselves [4]. Most chemical engineering books include chapters on catalytic reactions. In this paper, the main references used are the Chemical Reaction Engineering and Reactor Technology by Tapio Salmi, Jyri- Pekka Mikkola and Johan Wärnå and Chemical Reaction and Chemical Reactors by George W. Roberts. PROJECT DESCRIPTION The focus of this project is the study of the mass transport processes in a packed bed reactor. The external and internal mass transfer are studied separately. The amount of catalysts required for a specified reaction to reach 90% conversion is calculated for four different cases: (a) mass transfers processes are neglected (b) only the external mass transfer is considered (c) only the internal To simply the study and calculations, the following assumptions are considered: The reaction is run at isothermal conditions. Temperature differences in the catalyst are considered small enough that the coefficients are considered constant. The fluid is considered incompressible and thus the density is considered constant. The catalysts are assumed to be spherical. The amount of catalysts needed to reach 90% conversion is calculated by solving the transient equations describing the packed bed reactor. These transient equations change depending on the different cases considered. The different equations are presented and discussed in the following sections. Calculations are done using program MatLab. General transient equation To calculate the amount of catalyst (or catalyst mass, W cat (kg)) needed for a given conversion (X i), the mass balance equation must be solved. The general mass balance equation for a plug flow reactor is presented in equation 2. This equation is transformed to be in terms of the conversion and the amount of catalyst as presented in equations 3 to 5. Here, C i (mol/ m 3 ) is the reactant concentration, τ the residence time, V cat (m 3 ) is the total catalyst volume, G 0 (m 3 /s) the feed fluid flow rate and ρ cat (kg/m 3 ) the catalyst density. The feed concentration can also be expressed as shown is equation 6, where P 0 (atm) is the feed pressure, R the gas constant and T 0 (K) the feed temperature. 3
The explicit transient equation to be solved in MatLab can be derived from the previous equations. The expression is shown in equation (7). External mass transfer The external mass transfer can be modeled using Fick s Law as shown in equation 8, where N ext i (mol/m 2 s) is the external molar flux, D ext eff,i (m 2 /s) is the effective external diffusion coefficient and r (m) the film radius. The concentration gradient across the fluid film can be modeled using the expression in equation 9, where C b i and C s i (mol/ m 3 ) is the concentration in the bulk fluid and the catalyst surface respectively, and δ (m) is the film thickness [2]. The expression of the molar flux can then be simplified as shown in equation 10, where k G is the mass transfer coefficient [1]. The transient equation when the external mass transfer is considered is expressed in the same way as shown in equation 5. This is completed with equations 13 to 15 when solved in MatLab. The mass transfer coefficient for gasses k G (mol/m 2.s.atm) can be estimated using the correlation in equations 16. This is completed by other correlations expressed in equations 17 to 22 [6]. In these expressions, M (g/mol) is the mean molar mass, P (atm) the pressure, G(m 3 /s) the fluid flow rate, ρ f (kg/m 3 ) the fluid density, A (m 2 ) the cross section area of the reactor, Sc is Schmidt number, μ (Pa s) the fluid viscosity, D m (m 2 /s) the diffusion coefficient,v (m/s) is the axial velocity, Re is Reynold s number, d cat (m) is the catalyst diameter. The molar flux can also be expressed in terms of the partial pressures P b i and P s i (atm) by using the correlation expressed in equation 11. The new expression of the molar flux can then be expressed as shown in equation 12. Internal mass transfer Similarly to the external mass transfer, the internal mass transfer can also be modeled using Fick s Law as shown in equation 23 where N int i (mol/m 2 s) is the internal molar flux, D int eff,i (m 2 /s) is the effective internal diffusion coefficient. The general mass balance equation for a certain volume at steady state must be considered, which is expressed in equation 24. The balance equation can be developed for an infinitesimal volume to obtain the differential equation shown in equation 25, specifically applicable for spherical catalysts [2]. To determine the reaction rate when the external mass transfer is considered, it can be assumed that the all reactants diffused to the catalyst surface are converted. Thus, the reaction rate at steady state can be considered equal to the mass transfer rate as shown in equation 13. A cat (m 2 ) is the total area of the catalyst and ε is the catalyst porosity. The expression of the reaction rate changes as expressed in equation 14. The conversion can be expressed as shown in equation 15. 4 Solving a second- degree differential equation is more difficult. Another possible approach in evaluating the effects in the internal mass transfer is by using the effectiveness factor η. This serves as a correction factor for
the general reaction rate as shown in equation 26n, where r obs (mol/l s) is the observed reaction rate for the reactor [1]. The effectiveness factor can be estimated using the dimensionless parameter Thiele modulus ϕ as shown in equation 27 [1]. The expression of the Thiele modulus changes depending not only on the geometry of the catalyst but also the characteristics of the reaction [2]. The irreversible power law is used. The expression is shown in equation 28, where n is the degree of reaction and k the reaction rate coefficient [1]. For the considered reaction and catalyst form, the expression of the Thiele modulus is as shown in equation 29. When the external mass transfer is neglected, the concentration on the catalyst surface is equal to the concentration in the bulk (C s i= C b i). Fig. 4. Amount of catalyst for 90%: (a) mass transfer neglected, (b) with external mass transfer, (c) - - with internal mass transfer and (d) with both external and internal mass transfers. Table 2. Amount of catalyst for 90% conversion. The transient equation with the internal mass transfer considered is presented in equation 30. When both external and internal mass transfers are to be considered, the transient equation is as presented in equation 31. This is completed by the same equations for the external mass transfer, equations 13 to 15. Figure 4 shows the simulations obtained in MatLab for the four different cases considered. The amounts of catalyst needed for each case are presented in table 2. Neglecting mass transport resistances 3.4991 kg Considering external mass transport kg 4.7715 kg resistance Considering internal mass transport 31.3255 resistance Considering both mass transport resistances kg 32.3801 kg From the simulations curves, it can be observed that for the same amount of catalyst, a lower conversion is achieved when the mass transfer processes are considered. When the external mass transport is considered the amount of catalyst increases slightly. However when the internal mass transport in considered the amount of catalyst needed is increased 9 times. In the case studied, the internal mass transfer is more significant that the external mass transfer. It is clear that the internal mass transfer cannot be neglected when designing a rector for the considered process. If the mass transfers are neglected only 40% can be achieved for the calculated amount of catalyst. CONCLUSIONS Heterogeneous catalytic reactions are characterized with the use of solid catalyst. Most of these processes are run in packed bed reactors. For heterogeneous catalytic reactors, the transport processes are more significant. They should be taken into account when designing the reactor and estimating the efficacy of the process. Two regimes of mass transfer can be considered when dealing with solid catalyzed reactions: external and internal mass transfers. The external mass transfer can be described by the mass transfer coefficient k G. The effects of 5
the internal mass transfer can be evaluated by using the effectiveness factor η. When the mass transfer regimes are considered, the amount of catalyst required to achieve a given conversion increases. In the studied case, the dominating transfer processes is the internal mass transfer. However, it is possible for the external mass transfer to also become prominent depending on the specifications of the reaction and the process. Clearly, these transport processes influences a process considerably. Other considerations should also be looked into, such as the effects of temperature gradients. Not only does the temperature affect the reaction rate but the mass transfer coefficients can also be temperature dependent. REFERENCES [1] Roberts, G. W., 2009, Chemical reactions and chemical reactors, Hoboken, NJ : John Wiley & Sons, cop. Book [2] Salmi, T., Mikkola, J., & Wärnå, J., 2011, Catalytic Two- Phase Reactors in: Chemical reaction engineering and reactor technology; Johan Wärnå. Boca Raton, Fla.: CRC. Book chapter [3] Schmidt, L. D., 2005, The engineering of chemical reactions. New York: Oxford University Press. Book [4] Lloyd, L., 2006, Handbook of industrial catalyst, New York: Springer Science + Business Media. Book [5] Lidén, G., 2013, Chemical Reaction Engineering, advance course, Department of Chemical Engineering, LTH. Course [6] Froment, G. F., & Bischoff, K. B., 1990, Chemical reactor analysis and design,new York : Wiley, cop. Book 6